Patch-Based Image Restoration using Expectation Propagation

TL;DR

This paper introduces an Expectation Propagation framework for scalable, patch-based image restoration that efficiently approximates posterior distributions, enabling effective denoising, inpainting, and deconvolution with uncertainty quantification.

Contribution

The paper proposes a novel EP-based approach with structured covariance constraints for scalable, patch-based Bayesian image restoration, extending to non-Gaussian noise.

Findings

Effective denoising, inpainting, and deconvolution results.

Reduced computational cost compared to sampling methods.

Flexible handling of Gaussian and Poisson noise.

Abstract

This paper presents a new Expectation Propagation (EP) framework for image restoration using patch-based prior distributions. While Monte Carlo techniques are classically used to sample from intractable posterior distributions, they can suffer from scalability issues in high-dimensional inference problems such as image restoration. To address this issue, EP is used here to approximate the posterior distributions using products of multivariate Gaussian densities. Moreover, imposing structural constraints on the covariance matrices of these densities allows for greater scalability and distributed computation. While the method is naturally suited to handle additive Gaussian observation noise, it can also be extended to non-Gaussian noise. Experiments conducted for denoising, inpainting and deconvolution problems with Gaussian and Poisson noise illustrate the potential benefits of such flexible approximate Bayesian method for uncertainty quantification in imaging problems, at a reduced computational cost compared to sampling techniques.